Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 51.78 91.94
2 45.49 97.35
3 42.17 83.88
4 46.28 83.52
5 27.17 98.89

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 51.78 91.94 -40.16
2 45.49 97.35 -51.86
3 42.17 83.88 -41.71
4 46.28 83.52 -37.24
5 27.17 98.89 -71.72

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 91.94 NA
2 0 NA 97.35 NA
3 1 42.17 NA NA
4 0 NA 83.52 NA
5 0 NA 98.89 NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 51.78 91.94 -40.16
2 45.49 97.35 -51.86
3 42.17 83.88 -41.71
4 46.28 83.52 -37.24
5 27.17 98.89 -71.72

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
42.58 91.12 -48.54

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 91.94 NA
2 0 NA 97.35 NA
3 1 42.17 NA NA
4 0 NA 83.52 NA
5 0 NA 98.89 NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
42.17 92.92 -50.75

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 170.62 77.78 Brown
2 174.04 49.24 Brown
3 171.12 85.96 Grey
4 166.27 89.28 Grey
5 169.99 103.33 Brown
6 165.38 84.37 Brown
7 171.92 80.29 Green
8 173.02 97.12 Blue
9 165.83 91.32 Green
10 163.81 89.87 Brown
11 165.78 74.25 Green
12 175.28 99.72 Grey
13 171.90 95.85 Blue
14 171.11 63.92 Brown
15 167.29 66.29 Grey
16 167.43 97.85 Blue
17 166.59 77.91 Grey
18 169.54 89.53 Grey
19 162.91 81.23 Brown
20 156.62 71.98 Grey
21 168.07 83.66 Brown
22 167.72 81.11 Blue
23 173.65 78.10 Green
24 171.84 74.55 Grey
25 161.53 70.32 Brown
26 167.05 90.10 Brown
27 172.42 88.43 Blue
28 176.32 63.16 Grey
29 181.28 87.74 Green
30 171.20 63.42 Brown
31 166.78 74.78 Blue
32 168.40 80.77 Green
33 167.06 78.07 Grey
34 162.80 69.65 Blue
35 154.76 84.17 Brown
36 163.79 86.04 Brown
37 158.00 82.08 Green
38 170.47 68.50 Blue
39 170.56 77.96 Blue
40 180.94 94.93 Green
41 167.84 95.25 Brown
42 167.48 99.63 Brown
43 167.45 93.59 Grey
44 152.83 88.78 Grey
45 169.91 78.77 Grey
46 167.39 75.19 Green
47 163.90 77.07 Grey
48 171.55 75.64 Green
49 169.16 90.56 Grey
50 172.17 72.51 Blue
51 176.74 81.63 Blue
52 171.20 76.86 Blue
53 175.02 97.72 Blue
54 165.89 87.05 Green
55 159.78 76.90 Green
56 169.08 81.10 Brown
57 172.15 65.48 Brown
58 165.38 81.77 Green
59 164.43 81.79 Grey
60 174.78 74.47 Brown
61 182.01 74.23 Grey
62 166.11 79.51 Brown
63 174.10 90.42 Grey
64 174.12 82.12 Blue
65 169.17 91.05 Grey
66 181.42 77.08 Green
67 176.10 82.71 Brown
68 169.15 78.50 Grey
69 172.27 89.14 Blue
70 166.27 74.35 Green
71 168.44 70.31 Green
72 166.40 95.56 Grey
73 167.81 72.94 Brown
74 169.04 86.17 Green
75 170.34 74.29 Grey
76 173.59 85.34 Brown
77 160.20 83.85 Green
78 163.58 99.63 Blue
79 170.72 85.68 Grey
80 165.34 94.12 Brown
81 177.27 76.52 Green
82 157.97 69.20 Grey
83 180.20 93.03 Blue
84 164.41 80.35 Blue
85 171.17 87.68 Green
86 173.12 91.04 Brown
87 170.82 79.29 Brown
88 179.01 70.03 Green
89 173.40 85.50 Grey
90 153.63 85.02 Blue
91 157.98 81.01 Grey
92 177.32 90.66 Grey
93 169.64 64.72 Green
94 176.31 79.63 Blue
95 173.12 87.03 Green
96 181.55 94.48 Brown
97 164.51 77.91 Grey
98 173.67 70.98 Green
99 185.87 73.14 Blue
100 175.63 106.73 Green
101 170.16 63.49 Blue
102 161.98 92.24 Blue
103 164.81 64.20 Blue
104 171.76 91.59 Grey
105 173.45 79.38 Blue
106 178.81 85.98 Blue
107 169.10 92.82 Grey
108 166.88 91.30 Blue
109 173.63 78.75 Brown
110 173.67 54.60 Green
111 164.05 71.77 Grey
112 170.56 85.79 Green
113 161.59 65.32 Green
114 159.97 79.96 Green
115 167.57 86.89 Grey
116 165.20 86.76 Blue
117 162.48 55.40 Green
118 179.48 91.55 Blue
119 167.69 85.30 Blue
120 164.32 86.76 Blue
121 176.56 78.42 Green
122 166.03 68.93 Blue
123 175.66 91.10 Grey
124 173.17 95.23 Blue
125 175.84 100.18 Brown
126 163.15 75.93 Blue
127 170.37 86.70 Grey
128 174.11 85.43 Grey
129 164.79 85.64 Grey
130 170.73 76.34 Grey
131 186.59 70.37 Brown
132 165.57 75.13 Blue
133 169.04 67.44 Blue
134 175.40 101.61 Green
135 172.84 70.44 Blue
136 173.65 73.54 Brown
137 165.04 87.82 Green
138 178.02 82.15 Brown
139 170.15 82.39 Grey
140 167.53 68.22 Green
141 161.17 86.42 Blue
142 159.85 76.22 Green
143 177.30 64.93 Grey
144 170.08 91.70 Green
145 171.94 66.35 Grey
146 168.39 84.10 Green
147 181.65 83.92 Brown
148 162.03 63.61 Green
149 173.01 83.91 Green
150 167.48 94.82 Grey
151 162.33 75.85 Grey
152 173.18 75.34 Blue
153 174.91 96.38 Brown
154 167.47 90.25 Blue
155 174.41 94.96 Grey
156 174.90 78.69 Grey
157 171.82 72.72 Green
158 168.90 81.85 Grey
159 162.98 76.76 Brown
160 155.14 89.70 Blue
161 165.63 66.75 Blue
162 165.11 94.75 Grey
163 178.82 100.58 Brown
164 172.67 75.55 Brown
165 170.26 66.56 Green
166 167.62 84.77 Grey
167 163.63 55.40 Blue
168 165.41 79.29 Grey
169 174.51 70.43 Grey
170 180.01 70.95 Green
171 177.35 78.97 Blue
172 174.29 52.47 Green
173 166.63 78.44 Grey
174 180.02 75.06 Blue
175 168.21 93.89 Green
176 161.29 67.78 Brown
177 172.94 61.05 Green
178 166.38 89.27 Brown
179 175.07 82.56 Grey
180 170.23 87.77 Blue
181 175.95 92.22 Brown
182 169.59 78.52 Grey
183 174.96 78.73 Brown
184 172.37 83.49 Blue
185 175.60 77.63 Grey
186 177.30 56.96 Green
187 176.32 72.43 Brown
188 164.18 63.03 Green
189 164.53 76.59 Green
190 171.87 60.85 Green
191 172.65 98.63 Green
192 177.06 79.33 Blue
193 171.54 75.83 Brown
194 168.89 74.78 Blue
195 163.36 96.49 Grey
196 160.62 84.62 Grey
197 165.65 69.40 Blue
198 169.85 84.64 Green
199 156.28 74.89 Grey
200 174.21 86.76 Grey
201 170.00 86.61 Blue
202 159.73 76.70 Green
203 164.18 82.22 Blue
204 165.78 92.82 Brown
205 165.10 85.67 Green
206 172.86 83.77 Brown
207 169.74 73.18 Grey
208 175.94 81.90 Blue
209 162.98 84.52 Brown
210 159.15 73.38 Blue
211 169.32 73.60 Blue
212 154.14 71.95 Blue
213 172.24 75.03 Brown
214 154.08 90.05 Brown
215 167.74 91.83 Grey
216 170.58 76.46 Blue
217 166.15 77.12 Grey
218 178.03 89.99 Brown
219 164.31 95.61 Brown
220 178.09 87.15 Blue
221 168.28 76.83 Brown
222 178.79 69.79 Grey
223 163.44 82.43 Grey
224 175.38 72.01 Green
225 180.53 72.40 Grey
226 176.48 79.89 Grey
227 173.83 71.29 Brown
228 163.92 97.71 Blue
229 169.49 81.67 Green
230 167.89 76.51 Grey
231 164.06 77.95 Blue
232 177.57 60.08 Brown
233 170.36 93.87 Green
234 163.29 78.48 Brown
235 162.85 84.71 Brown
236 159.09 75.07 Blue
237 171.42 65.11 Blue
238 168.34 83.67 Grey
239 172.22 80.99 Blue
240 166.33 83.19 Blue
241 174.84 85.51 Grey
242 165.34 69.62 Green
243 169.36 79.82 Green
244 179.62 93.70 Brown
245 169.82 84.24 Blue
246 166.66 83.28 Green
247 161.48 85.71 Green
248 157.12 77.46 Blue
249 180.87 76.46 Green
250 165.45 74.02 Grey
251 174.05 90.16 Grey
252 169.76 82.22 Brown
253 163.57 88.21 Brown
254 169.04 79.57 Green
255 166.77 86.78 Green
256 177.32 81.80 Blue
257 174.64 79.11 Green
258 157.93 71.06 Blue
259 166.43 84.81 Green
260 181.11 95.02 Grey
261 175.02 64.48 Green
262 166.49 75.80 Blue
263 172.96 101.45 Brown
264 167.46 77.60 Brown
265 171.88 99.65 Blue
266 169.96 76.15 Blue
267 171.61 69.22 Brown
268 173.93 77.01 Grey
269 175.86 87.87 Brown
270 163.80 79.77 Brown
271 162.62 89.06 Brown
272 164.56 81.04 Blue
273 169.15 78.08 Blue
274 178.99 82.12 Blue
275 172.16 79.83 Blue
276 177.58 64.16 Blue
277 172.11 87.64 Blue
278 172.05 80.89 Green
279 158.79 88.85 Grey
280 164.65 76.36 Grey
281 158.25 85.47 Blue
282 161.47 86.85 Grey
283 168.93 74.24 Blue
284 173.54 81.79 Grey
285 168.52 71.50 Grey
286 175.56 79.94 Blue
287 171.62 108.83 Blue
288 181.84 68.46 Brown
289 158.44 86.19 Blue
290 176.02 82.23 Green
291 168.42 84.62 Green
292 173.19 83.46 Grey
293 166.54 85.19 Brown
294 151.38 81.86 Grey
295 168.90 88.59 Green
296 172.88 90.38 Blue
297 163.58 86.98 Green
298 171.87 72.61 Brown
299 155.50 86.58 Grey
300 161.69 77.95 Green
301 163.56 83.34 Blue
302 156.77 83.00 Grey
303 179.06 81.64 Blue
304 160.63 79.35 Blue
305 179.69 80.81 Brown
306 177.41 80.01 Brown
307 171.50 77.46 Green
308 165.03 95.09 Grey
309 165.97 73.05 Blue
310 174.97 88.43 Brown
311 166.61 69.08 Green
312 167.91 87.84 Blue
313 169.47 56.45 Blue
314 167.06 72.44 Brown
315 169.09 85.62 Brown
316 176.48 84.64 Green
317 169.26 77.97 Brown
318 166.44 81.41 Blue
319 167.66 97.88 Brown
320 177.46 86.76 Grey
321 167.35 87.24 Green
322 172.86 73.35 Grey
323 177.16 89.08 Grey
324 165.88 90.44 Green
325 167.17 85.64 Blue
326 183.38 55.84 Grey
327 169.61 84.00 Grey
328 169.70 85.50 Green
329 166.65 82.95 Grey
330 164.89 82.81 Blue
331 158.82 74.39 Grey
332 168.01 88.06 Brown
333 165.09 76.29 Brown
334 180.56 75.08 Blue
335 167.27 77.80 Blue
336 173.88 69.05 Blue
337 168.97 77.02 Brown
338 173.34 73.76 Brown
339 176.46 87.81 Grey
340 169.78 94.35 Green
341 169.27 59.98 Grey
342 173.28 75.23 Green
343 175.18 97.06 Blue
344 169.39 73.95 Brown
345 172.04 70.90 Brown
346 161.62 96.00 Grey
347 167.23 89.55 Grey
348 168.43 76.65 Grey
349 165.32 81.25 Brown
350 170.01 70.74 Green
351 173.34 68.53 Green
352 176.02 77.40 Blue
353 180.56 78.09 Blue
354 170.24 80.80 Blue
355 158.60 103.87 Green
356 174.98 78.75 Grey
357 168.61 72.29 Green
358 170.10 68.90 Blue
359 174.01 77.02 Blue
360 164.99 72.64 Grey
361 159.98 83.14 Grey
362 175.54 96.49 Green
363 179.56 96.62 Grey
364 165.69 91.31 Blue
365 173.79 85.11 Green
366 187.49 100.73 Brown
367 160.26 76.32 Green
368 173.90 73.22 Green
369 172.34 87.56 Brown
370 167.85 71.15 Brown
371 164.94 78.22 Blue
372 168.43 100.49 Green
373 170.77 61.10 Green
374 165.16 94.65 Grey
375 181.06 82.71 Blue
376 180.98 69.60 Green
377 165.63 102.78 Brown
378 173.88 84.07 Blue
379 161.95 77.01 Green
380 154.79 90.84 Brown
381 172.77 86.06 Brown
382 167.95 80.49 Blue
383 172.97 101.62 Grey
384 171.57 87.71 Grey
385 176.72 75.32 Blue
386 164.06 87.94 Green
387 172.79 83.01 Blue
388 175.86 75.64 Brown
389 167.42 92.96 Blue
390 162.53 65.76 Green
391 168.44 74.42 Green
392 167.32 84.70 Brown
393 182.32 69.11 Blue
394 165.47 77.11 Grey
395 173.39 78.83 Brown
396 176.25 63.43 Grey
397 172.76 78.82 Brown
398 165.97 87.00 Brown
399 161.92 72.14 Blue
400 170.86 74.11 Green
401 167.52 92.29 Grey
402 164.94 84.64 Green
403 168.27 79.70 Blue
404 171.15 79.21 Grey
405 175.77 74.46 Blue
406 168.97 89.02 Brown
407 158.81 80.27 Blue
408 174.03 89.98 Brown
409 169.40 86.23 Grey
410 165.39 71.14 Grey
411 169.39 69.60 Blue
412 169.70 64.77 Grey
413 169.33 55.84 Green
414 166.31 66.28 Blue
415 171.87 82.67 Blue
416 169.81 85.32 Blue
417 165.96 98.49 Brown
418 170.11 82.69 Green
419 172.79 71.13 Green
420 151.57 74.58 Green
421 170.07 77.48 Blue
422 175.22 86.84 Grey
423 167.23 83.74 Blue
424 167.22 71.24 Green
425 170.32 75.31 Blue
426 171.78 73.14 Brown
427 167.27 59.76 Grey
428 171.14 86.26 Brown
429 163.64 86.49 Blue
430 168.21 80.75 Blue
431 173.15 90.29 Brown
432 179.22 77.37 Brown
433 167.71 87.98 Brown
434 164.39 72.47 Grey
435 162.67 92.86 Green
436 167.86 82.60 Brown
437 175.16 89.60 Blue
438 171.33 76.94 Grey
439 170.80 92.12 Blue
440 153.98 63.60 Blue
441 176.48 91.12 Brown
442 165.54 86.03 Grey
443 170.35 71.17 Grey
444 164.12 69.42 Green
445 166.53 92.79 Blue
446 161.65 80.08 Grey
447 162.83 71.39 Grey
448 154.30 73.71 Blue
449 171.31 96.96 Grey
450 170.92 92.17 Grey
451 176.17 80.38 Blue
452 164.79 85.05 Grey
453 172.76 89.85 Blue
454 172.17 90.20 Grey
455 169.22 80.94 Blue
456 174.34 89.89 Grey
457 159.21 85.14 Green
458 159.25 84.37 Brown
459 178.79 85.92 Brown
460 170.75 100.58 Green
461 174.01 87.50 Green
462 170.14 60.14 Blue
463 166.26 92.74 Grey
464 158.56 86.13 Blue
465 172.19 66.96 Brown
466 180.26 58.91 Green
467 173.94 76.43 Green
468 174.47 82.83 Brown
469 174.15 75.78 Green
470 178.28 77.57 Blue
471 167.32 76.81 Brown
472 167.55 74.71 Brown
473 174.61 80.27 Green
474 173.82 76.83 Blue
475 167.19 79.44 Green
476 177.24 93.01 Blue
477 176.86 82.12 Green
478 179.92 65.61 Blue
479 172.28 93.04 Green
480 171.46 89.48 Green
481 172.67 79.50 Green
482 166.06 77.27 Green
483 176.50 77.26 Brown
484 156.14 92.50 Blue
485 174.33 63.12 Green
486 165.67 86.60 Brown
487 182.18 67.37 Green
488 168.91 86.88 Brown
489 168.06 81.96 Blue
490 168.13 89.14 Green
491 165.28 79.44 Grey
492 162.20 80.96 Green
493 168.13 102.88 Grey
494 167.04 82.09 Brown
495 171.84 77.24 Grey
496 184.84 88.92 Green
497 163.31 75.80 Grey
498 168.68 62.92 Blue
499 164.68 87.64 Brown
500 168.44 80.81 Brown
501 170.56 79.15 Grey
502 170.47 80.63 Brown
503 175.32 78.17 Grey
504 158.59 74.18 Brown
505 165.56 80.54 Grey
506 169.45 94.18 Green
507 178.75 85.72 Green
508 162.96 74.55 Grey
509 178.21 73.44 Blue
510 174.59 72.40 Blue
511 165.34 56.60 Blue
512 163.03 86.26 Brown
513 169.64 95.38 Grey
514 164.10 70.94 Blue
515 176.51 62.65 Green
516 171.61 78.36 Blue
517 172.94 84.12 Brown
518 171.89 87.12 Green
519 170.93 94.28 Green
520 177.57 67.06 Green
521 160.03 78.09 Green
522 169.60 88.06 Green
523 173.22 78.78 Grey
524 170.88 93.96 Blue
525 176.22 85.53 Grey
526 161.18 80.51 Brown
527 177.53 71.20 Green
528 169.75 59.59 Brown
529 176.47 72.47 Green
530 169.93 73.92 Brown
531 171.35 88.80 Brown
532 154.61 87.71 Green
533 169.48 100.93 Blue
534 159.87 83.71 Brown
535 181.63 71.47 Blue
536 172.27 76.68 Green
537 169.75 91.72 Brown
538 172.92 84.89 Blue
539 168.23 96.27 Blue
540 170.28 99.65 Grey
541 178.00 93.20 Green
542 167.68 78.06 Green
543 178.57 75.86 Grey
544 161.43 90.47 Blue
545 168.57 87.13 Green
546 169.03 78.56 Brown
547 176.40 69.67 Grey
548 164.51 73.67 Grey
549 175.72 98.95 Brown
550 164.30 86.90 Grey
551 179.74 75.47 Grey
552 169.85 89.23 Blue
553 164.25 87.27 Green
554 163.10 76.19 Grey
555 175.64 88.12 Brown
556 169.75 73.06 Green
557 163.19 95.33 Brown
558 163.43 87.91 Grey
559 170.85 107.88 Brown
560 175.98 66.96 Grey
561 174.14 79.59 Grey
562 164.63 93.77 Brown
563 171.05 83.14 Grey
564 175.30 80.91 Blue
565 171.79 77.92 Green
566 190.44 81.94 Blue
567 162.78 81.46 Blue
568 164.60 77.69 Blue
569 178.35 67.43 Grey
570 171.65 78.93 Brown
571 177.71 89.10 Brown
572 176.95 78.05 Grey
573 172.74 70.49 Blue
574 176.61 77.40 Blue
575 168.20 77.70 Green
576 177.16 76.00 Green
577 163.80 80.86 Blue
578 175.10 82.01 Grey
579 163.18 75.15 Blue
580 163.82 75.95 Blue
581 177.32 78.83 Grey
582 174.91 71.80 Grey
583 166.34 70.16 Green
584 175.25 65.76 Brown
585 156.16 86.63 Green
586 166.14 69.57 Green
587 161.35 82.06 Blue
588 164.37 68.86 Green
589 164.92 76.66 Blue
590 174.23 82.38 Brown
591 174.52 70.99 Grey
592 186.73 77.90 Brown
593 176.61 66.73 Brown
594 178.36 79.33 Blue
595 179.95 88.37 Green
596 162.99 67.45 Green
597 161.19 69.84 Blue
598 166.66 73.27 Blue
599 166.08 76.23 Grey
600 162.38 93.61 Green
601 156.36 93.38 Blue
602 173.69 82.56 Brown
603 177.88 71.49 Green
604 162.75 71.58 Blue
605 155.25 79.86 Brown
606 173.30 74.63 Blue
607 171.15 85.35 Blue
608 174.29 81.74 Blue
609 166.11 77.77 Grey
610 177.69 71.63 Grey
611 176.83 97.28 Green
612 173.63 66.37 Grey
613 168.13 84.93 Green
614 186.67 89.01 Blue
615 169.45 91.76 Blue
616 178.85 64.77 Blue
617 161.17 68.79 Grey
618 167.75 63.01 Green
619 171.41 88.07 Grey
620 160.24 79.17 Grey
621 170.00 84.39 Grey
622 172.43 90.57 Blue
623 178.24 82.11 Green
624 174.22 85.25 Brown
625 180.30 77.02 Green
626 174.27 89.12 Brown
627 170.56 82.55 Green
628 176.39 76.38 Grey
629 163.32 65.88 Green
630 170.75 74.43 Grey
631 160.66 61.51 Blue
632 172.63 83.80 Brown
633 166.59 92.43 Blue
634 169.93 67.27 Green
635 175.05 77.63 Grey
636 178.56 60.04 Blue
637 168.06 66.69 Grey
638 170.22 73.47 Blue
639 176.07 75.65 Blue
640 166.89 70.63 Blue
641 167.15 62.59 Blue
642 168.53 79.38 Blue
643 172.10 74.06 Grey
644 174.17 63.32 Grey
645 174.77 87.55 Grey
646 176.97 80.21 Blue
647 164.17 79.90 Grey
648 171.23 71.95 Grey
649 178.24 71.82 Green
650 153.72 72.64 Brown
651 162.70 82.01 Brown
652 170.51 89.57 Green
653 163.95 68.58 Brown
654 162.51 83.46 Grey
655 164.24 82.45 Brown
656 167.54 83.40 Brown
657 180.75 81.15 Blue
658 169.94 91.08 Brown
659 174.52 73.70 Brown
660 163.22 95.60 Brown
661 175.33 74.50 Green
662 171.08 62.38 Brown
663 171.09 77.07 Blue
664 170.31 66.84 Brown
665 172.64 95.30 Brown
666 174.63 76.54 Blue
667 169.94 84.62 Brown
668 176.14 63.09 Brown
669 174.21 66.37 Grey
670 172.13 84.67 Brown
671 169.09 84.65 Brown
672 169.38 74.12 Blue
673 168.05 82.06 Brown
674 162.81 88.53 Brown
675 171.95 88.09 Blue
676 170.11 73.98 Brown
677 175.39 91.79 Green
678 174.19 82.75 Green
679 167.34 86.30 Brown
680 168.52 98.53 Blue
681 176.53 92.44 Brown
682 166.62 78.45 Blue
683 161.31 62.22 Grey
684 166.47 70.96 Blue
685 180.05 73.98 Blue
686 168.94 89.70 Green
687 169.79 80.33 Blue
688 168.25 74.68 Blue
689 164.29 82.73 Blue
690 171.67 91.56 Brown
691 174.31 77.22 Brown
692 172.06 71.97 Blue
693 161.57 72.75 Blue
694 164.84 76.83 Blue
695 172.66 67.10 Green
696 162.87 49.90 Blue
697 163.19 78.14 Brown
698 164.02 96.30 Green
699 183.65 99.65 Brown
700 175.41 82.76 Brown
701 174.07 80.72 Blue
702 174.03 94.90 Brown
703 167.99 56.45 Brown
704 173.09 78.02 Green
705 171.77 99.21 Brown
706 179.12 73.48 Green
707 174.09 70.61 Blue
708 161.14 77.89 Grey
709 174.88 73.97 Blue
710 170.58 73.96 Blue
711 170.48 80.32 Grey
712 179.76 93.34 Green
713 170.23 85.36 Blue
714 168.76 87.17 Blue
715 172.88 81.29 Green
716 172.18 89.87 Green
717 171.80 76.74 Brown
718 166.94 73.91 Brown
719 165.70 90.13 Green
720 171.07 70.05 Blue
721 164.01 66.34 Blue
722 168.21 70.46 Brown
723 171.18 79.93 Brown
724 164.36 78.43 Brown
725 166.96 95.54 Blue
726 163.79 87.12 Blue
727 165.65 70.37 Brown
728 175.15 81.44 Grey
729 174.15 84.45 Brown
730 180.04 92.50 Green
731 170.75 92.74 Blue
732 168.77 88.26 Brown
733 164.22 71.09 Green
734 162.97 76.52 Brown
735 176.71 77.90 Grey
736 176.80 71.54 Blue
737 165.90 90.97 Green
738 172.60 79.67 Blue
739 167.44 80.15 Grey
740 165.58 90.47 Blue
741 173.97 68.93 Green
742 171.99 75.40 Grey
743 172.34 78.00 Green
744 179.89 103.31 Blue
745 167.02 74.14 Blue
746 172.16 54.04 Blue
747 176.38 70.12 Grey
748 170.93 82.14 Grey
749 167.08 91.17 Brown
750 164.93 82.62 Blue
751 175.88 76.24 Grey
752 166.28 83.51 Brown
753 170.95 75.33 Green
754 179.68 66.80 Green
755 169.16 93.42 Brown
756 168.96 90.89 Blue
757 163.47 93.37 Brown
758 171.15 71.93 Brown
759 167.40 75.02 Blue
760 161.63 102.45 Grey
761 180.13 77.66 Brown
762 178.47 80.87 Blue
763 169.63 75.21 Grey
764 176.56 86.78 Green
765 177.74 82.43 Grey
766 169.19 69.64 Green
767 164.83 97.09 Brown
768 163.19 89.89 Blue
769 165.76 85.69 Blue
770 173.29 72.52 Green
771 167.18 77.84 Grey
772 172.95 78.55 Green
773 176.74 74.88 Blue
774 177.22 87.75 Grey
775 166.53 74.29 Green
776 160.60 67.70 Green
777 176.38 88.54 Green
778 174.40 85.31 Brown
779 165.25 91.00 Green
780 177.43 89.33 Blue
781 167.65 63.56 Green
782 177.33 94.90 Grey
783 170.09 86.71 Green
784 165.35 77.97 Green
785 170.60 76.48 Grey
786 162.26 67.41 Green
787 167.22 84.14 Green
788 175.02 74.77 Green
789 168.25 82.26 Brown
790 179.58 82.23 Brown
791 166.60 63.60 Grey
792 183.53 93.09 Green
793 162.68 87.86 Blue
794 162.25 78.41 Grey
795 166.39 86.34 Blue
796 168.94 76.32 Grey
797 169.38 66.64 Green
798 160.81 80.23 Brown
799 175.86 103.65 Blue
800 173.55 75.50 Green
801 175.93 78.76 Brown
802 174.23 72.99 Green
803 155.07 78.15 Brown
804 154.94 91.89 Green
805 181.97 85.87 Blue
806 168.37 78.18 Blue
807 168.38 84.86 Grey
808 164.10 86.29 Brown
809 176.51 83.06 Brown
810 169.17 70.59 Blue
811 165.30 88.88 Green
812 152.73 106.71 Grey
813 162.30 78.38 Grey
814 169.78 88.09 Green
815 156.24 69.05 Brown
816 173.76 84.85 Brown
817 167.88 68.38 Grey
818 173.61 80.97 Brown
819 173.97 65.25 Brown
820 170.20 72.93 Green
821 163.11 76.60 Green
822 168.18 79.78 Green
823 180.30 74.17 Brown
824 178.59 108.06 Grey
825 175.04 93.19 Blue
826 166.47 83.47 Green
827 167.79 103.34 Green
828 168.53 87.19 Green
829 173.41 85.98 Green
830 177.26 71.78 Green
831 165.19 73.09 Grey
832 160.25 79.25 Brown
833 166.17 75.82 Blue
834 165.99 90.73 Brown
835 174.01 93.04 Grey
836 170.75 73.70 Green
837 165.53 76.12 Grey
838 163.12 79.36 Brown
839 175.52 104.40 Grey
840 162.10 82.79 Grey
841 170.70 81.55 Grey
842 179.68 80.26 Grey
843 173.63 74.21 Blue
844 164.29 95.37 Blue
845 176.13 65.54 Grey
846 166.36 95.99 Blue
847 159.11 95.86 Grey
848 161.11 82.53 Green
849 168.29 75.64 Blue
850 169.12 92.68 Grey
851 178.47 79.49 Blue
852 164.98 84.26 Brown
853 167.15 91.39 Brown
854 174.75 89.21 Blue
855 173.06 96.82 Grey
856 170.89 85.34 Green
857 176.36 81.04 Green
858 159.71 89.90 Green
859 179.42 74.60 Brown
860 171.31 77.28 Brown
861 175.87 79.65 Grey
862 172.01 73.07 Green
863 172.25 88.08 Green
864 174.65 103.53 Grey
865 169.25 87.58 Blue
866 174.45 76.70 Grey
867 168.06 73.86 Green
868 168.20 94.57 Brown
869 174.37 83.11 Brown
870 177.28 84.83 Green
871 161.53 68.31 Blue
872 176.04 82.64 Blue
873 168.29 89.21 Brown
874 171.79 84.39 Grey
875 161.65 64.42 Grey
876 167.76 72.40 Blue
877 165.00 85.91 Blue
878 169.62 86.85 Green
879 164.89 86.33 Brown
880 172.45 92.88 Blue
881 177.68 82.90 Grey
882 171.01 73.70 Brown
883 172.80 70.30 Green
884 162.82 78.72 Grey
885 172.07 78.42 Brown
886 167.53 76.82 Green
887 166.53 61.72 Brown
888 175.83 82.41 Brown
889 175.85 78.54 Blue
890 172.35 77.06 Green
891 159.89 72.25 Blue
892 168.86 74.20 Green
893 168.82 84.83 Grey
894 162.43 76.83 Grey
895 171.67 78.62 Green
896 170.28 84.15 Grey
897 164.97 92.02 Grey
898 173.88 79.34 Grey
899 169.67 89.66 Blue
900 161.69 75.16 Blue
901 172.27 85.13 Brown
902 169.54 91.62 Green
903 168.60 77.12 Grey
904 182.19 95.20 Brown
905 168.41 96.50 Grey
906 172.94 88.94 Green
907 161.49 74.56 Green
908 173.85 76.79 Green
909 174.67 68.89 Blue
910 170.00 79.42 Green
911 173.66 69.17 Grey
912 171.71 75.47 Green
913 176.86 86.89 Brown
914 177.43 83.44 Grey
915 176.72 87.39 Grey
916 163.52 85.04 Green
917 167.98 64.71 Blue
918 169.84 68.25 Brown
919 181.70 86.95 Grey
920 168.66 87.02 Green
921 178.01 76.09 Grey
922 172.97 86.43 Blue
923 163.88 94.98 Blue
924 175.91 70.74 Green
925 175.02 83.33 Grey
926 166.03 74.03 Grey
927 168.75 68.48 Grey
928 169.23 91.66 Grey
929 180.73 84.52 Blue
930 171.83 84.99 Brown
931 175.38 84.91 Brown
932 174.40 68.84 Grey
933 169.82 84.77 Grey
934 167.19 86.10 Brown
935 179.94 82.12 Blue
936 164.61 83.94 Brown
937 165.90 80.76 Green
938 168.49 62.05 Green
939 171.94 62.71 Blue
940 166.10 70.15 Green
941 179.36 67.38 Grey
942 170.49 72.80 Green
943 169.66 72.84 Brown
944 165.70 67.24 Green
945 167.07 69.70 Green
946 167.18 85.68 Green
947 176.69 71.44 Blue
948 167.44 82.49 Green
949 174.51 86.17 Grey
950 165.77 80.27 Brown
951 159.22 69.53 Brown
952 158.99 81.21 Grey
953 167.96 94.78 Blue
954 166.47 57.39 Blue
955 165.49 77.38 Grey
956 161.26 77.51 Brown
957 171.96 71.25 Brown
958 171.74 74.65 Blue
959 165.00 64.00 Grey
960 175.32 94.93 Grey
961 168.47 70.10 Brown
962 169.96 76.55 Green
963 159.99 85.83 Brown
964 182.92 68.42 Blue
965 166.44 77.82 Grey
966 168.62 79.84 Grey
967 172.09 61.65 Blue
968 175.73 76.45 Brown
969 168.53 93.80 Blue
970 156.00 90.44 Grey
971 166.66 60.89 Brown
972 161.20 56.18 Green
973 179.80 77.04 Brown
974 164.49 82.16 Green
975 164.97 77.10 Green
976 166.25 72.15 Blue
977 165.78 84.93 Blue
978 159.43 77.98 Green
979 165.40 108.75 Grey
980 168.26 83.79 Grey
981 171.39 91.25 Grey
982 176.38 70.61 Green
983 174.40 85.17 Grey
984 169.76 73.37 Green
985 158.29 96.39 Grey
986 177.91 83.13 Grey
987 167.58 72.57 Green
988 158.10 67.28 Grey
989 170.73 95.74 Brown
990 165.32 89.17 Brown
991 175.11 72.74 Grey
992 167.17 88.95 Green
993 172.26 104.35 Grey
994 162.35 60.29 Brown
995 162.48 90.76 Green
996 174.42 85.16 Blue
997 169.26 72.03 Brown
998 178.41 75.57 Grey
999 167.06 77.55 Blue
1000 169.07 92.08 Blue

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 170.62 77.78 Brown A
2 174.04 49.24 Brown A
3 171.12 85.96 Grey A
4 166.27 89.28 Grey B
5 169.99 103.33 Brown A
6 165.38 84.37 Brown B
7 171.92 80.29 Green A
8 173.02 97.12 Blue A
9 165.83 91.32 Green B
10 163.81 89.87 Brown A
11 165.78 74.25 Green B
12 175.28 99.72 Grey B
13 171.90 95.85 Blue B
14 171.11 63.92 Brown B
15 167.29 66.29 Grey B
16 167.43 97.85 Blue B
17 166.59 77.91 Grey B
18 169.54 89.53 Grey A
19 162.91 81.23 Brown B
20 156.62 71.98 Grey B
21 168.07 83.66 Brown B
22 167.72 81.11 Blue A
23 173.65 78.10 Green A
24 171.84 74.55 Grey A
25 161.53 70.32 Brown A
26 167.05 90.10 Brown B
27 172.42 88.43 Blue A
28 176.32 63.16 Grey A
29 181.28 87.74 Green B
30 171.20 63.42 Brown B
31 166.78 74.78 Blue B
32 168.40 80.77 Green A
33 167.06 78.07 Grey B
34 162.80 69.65 Blue A
35 154.76 84.17 Brown A
36 163.79 86.04 Brown B
37 158.00 82.08 Green B
38 170.47 68.50 Blue A
39 170.56 77.96 Blue B
40 180.94 94.93 Green A
41 167.84 95.25 Brown A
42 167.48 99.63 Brown A
43 167.45 93.59 Grey A
44 152.83 88.78 Grey A
45 169.91 78.77 Grey A
46 167.39 75.19 Green A
47 163.90 77.07 Grey B
48 171.55 75.64 Green B
49 169.16 90.56 Grey B
50 172.17 72.51 Blue A
51 176.74 81.63 Blue A
52 171.20 76.86 Blue A
53 175.02 97.72 Blue B
54 165.89 87.05 Green B
55 159.78 76.90 Green A
56 169.08 81.10 Brown B
57 172.15 65.48 Brown B
58 165.38 81.77 Green B
59 164.43 81.79 Grey A
60 174.78 74.47 Brown A
61 182.01 74.23 Grey B
62 166.11 79.51 Brown A
63 174.10 90.42 Grey A
64 174.12 82.12 Blue A
65 169.17 91.05 Grey B
66 181.42 77.08 Green B
67 176.10 82.71 Brown A
68 169.15 78.50 Grey B
69 172.27 89.14 Blue A
70 166.27 74.35 Green A
71 168.44 70.31 Green A
72 166.40 95.56 Grey B
73 167.81 72.94 Brown A
74 169.04 86.17 Green A
75 170.34 74.29 Grey B
76 173.59 85.34 Brown B
77 160.20 83.85 Green B
78 163.58 99.63 Blue A
79 170.72 85.68 Grey B
80 165.34 94.12 Brown A
81 177.27 76.52 Green B
82 157.97 69.20 Grey A
83 180.20 93.03 Blue A
84 164.41 80.35 Blue B
85 171.17 87.68 Green B
86 173.12 91.04 Brown A
87 170.82 79.29 Brown A
88 179.01 70.03 Green B
89 173.40 85.50 Grey B
90 153.63 85.02 Blue A
91 157.98 81.01 Grey B
92 177.32 90.66 Grey A
93 169.64 64.72 Green B
94 176.31 79.63 Blue A
95 173.12 87.03 Green B
96 181.55 94.48 Brown A
97 164.51 77.91 Grey A
98 173.67 70.98 Green A
99 185.87 73.14 Blue B
100 175.63 106.73 Green A
101 170.16 63.49 Blue A
102 161.98 92.24 Blue A
103 164.81 64.20 Blue A
104 171.76 91.59 Grey B
105 173.45 79.38 Blue B
106 178.81 85.98 Blue B
107 169.10 92.82 Grey B
108 166.88 91.30 Blue A
109 173.63 78.75 Brown B
110 173.67 54.60 Green B
111 164.05 71.77 Grey B
112 170.56 85.79 Green A
113 161.59 65.32 Green B
114 159.97 79.96 Green A
115 167.57 86.89 Grey B
116 165.20 86.76 Blue A
117 162.48 55.40 Green A
118 179.48 91.55 Blue B
119 167.69 85.30 Blue B
120 164.32 86.76 Blue B
121 176.56 78.42 Green A
122 166.03 68.93 Blue B
123 175.66 91.10 Grey A
124 173.17 95.23 Blue A
125 175.84 100.18 Brown A
126 163.15 75.93 Blue A
127 170.37 86.70 Grey A
128 174.11 85.43 Grey B
129 164.79 85.64 Grey B
130 170.73 76.34 Grey A
131 186.59 70.37 Brown B
132 165.57 75.13 Blue A
133 169.04 67.44 Blue B
134 175.40 101.61 Green B
135 172.84 70.44 Blue B
136 173.65 73.54 Brown A
137 165.04 87.82 Green B
138 178.02 82.15 Brown B
139 170.15 82.39 Grey A
140 167.53 68.22 Green A
141 161.17 86.42 Blue B
142 159.85 76.22 Green A
143 177.30 64.93 Grey A
144 170.08 91.70 Green B
145 171.94 66.35 Grey A
146 168.39 84.10 Green A
147 181.65 83.92 Brown A
148 162.03 63.61 Green A
149 173.01 83.91 Green A
150 167.48 94.82 Grey B
151 162.33 75.85 Grey B
152 173.18 75.34 Blue A
153 174.91 96.38 Brown B
154 167.47 90.25 Blue B
155 174.41 94.96 Grey A
156 174.90 78.69 Grey B
157 171.82 72.72 Green A
158 168.90 81.85 Grey A
159 162.98 76.76 Brown B
160 155.14 89.70 Blue B
161 165.63 66.75 Blue A
162 165.11 94.75 Grey B
163 178.82 100.58 Brown A
164 172.67 75.55 Brown B
165 170.26 66.56 Green B
166 167.62 84.77 Grey B
167 163.63 55.40 Blue B
168 165.41 79.29 Grey B
169 174.51 70.43 Grey B
170 180.01 70.95 Green B
171 177.35 78.97 Blue B
172 174.29 52.47 Green B
173 166.63 78.44 Grey B
174 180.02 75.06 Blue B
175 168.21 93.89 Green B
176 161.29 67.78 Brown B
177 172.94 61.05 Green B
178 166.38 89.27 Brown A
179 175.07 82.56 Grey B
180 170.23 87.77 Blue A
181 175.95 92.22 Brown B
182 169.59 78.52 Grey A
183 174.96 78.73 Brown B
184 172.37 83.49 Blue A
185 175.60 77.63 Grey B
186 177.30 56.96 Green A
187 176.32 72.43 Brown A
188 164.18 63.03 Green A
189 164.53 76.59 Green A
190 171.87 60.85 Green B
191 172.65 98.63 Green A
192 177.06 79.33 Blue A
193 171.54 75.83 Brown A
194 168.89 74.78 Blue B
195 163.36 96.49 Grey A
196 160.62 84.62 Grey A
197 165.65 69.40 Blue A
198 169.85 84.64 Green A
199 156.28 74.89 Grey A
200 174.21 86.76 Grey A
201 170.00 86.61 Blue B
202 159.73 76.70 Green B
203 164.18 82.22 Blue B
204 165.78 92.82 Brown A
205 165.10 85.67 Green A
206 172.86 83.77 Brown B
207 169.74 73.18 Grey A
208 175.94 81.90 Blue A
209 162.98 84.52 Brown B
210 159.15 73.38 Blue B
211 169.32 73.60 Blue B
212 154.14 71.95 Blue A
213 172.24 75.03 Brown A
214 154.08 90.05 Brown B
215 167.74 91.83 Grey A
216 170.58 76.46 Blue B
217 166.15 77.12 Grey B
218 178.03 89.99 Brown B
219 164.31 95.61 Brown A
220 178.09 87.15 Blue A
221 168.28 76.83 Brown A
222 178.79 69.79 Grey A
223 163.44 82.43 Grey B
224 175.38 72.01 Green B
225 180.53 72.40 Grey A
226 176.48 79.89 Grey A
227 173.83 71.29 Brown A
228 163.92 97.71 Blue A
229 169.49 81.67 Green A
230 167.89 76.51 Grey A
231 164.06 77.95 Blue A
232 177.57 60.08 Brown A
233 170.36 93.87 Green A
234 163.29 78.48 Brown B
235 162.85 84.71 Brown B
236 159.09 75.07 Blue A
237 171.42 65.11 Blue A
238 168.34 83.67 Grey A
239 172.22 80.99 Blue A
240 166.33 83.19 Blue B
241 174.84 85.51 Grey B
242 165.34 69.62 Green A
243 169.36 79.82 Green A
244 179.62 93.70 Brown B
245 169.82 84.24 Blue A
246 166.66 83.28 Green B
247 161.48 85.71 Green B
248 157.12 77.46 Blue A
249 180.87 76.46 Green B
250 165.45 74.02 Grey B
251 174.05 90.16 Grey B
252 169.76 82.22 Brown B
253 163.57 88.21 Brown B
254 169.04 79.57 Green B
255 166.77 86.78 Green A
256 177.32 81.80 Blue A
257 174.64 79.11 Green A
258 157.93 71.06 Blue A
259 166.43 84.81 Green A
260 181.11 95.02 Grey A
261 175.02 64.48 Green A
262 166.49 75.80 Blue A
263 172.96 101.45 Brown B
264 167.46 77.60 Brown A
265 171.88 99.65 Blue B
266 169.96 76.15 Blue B
267 171.61 69.22 Brown B
268 173.93 77.01 Grey B
269 175.86 87.87 Brown A
270 163.80 79.77 Brown A
271 162.62 89.06 Brown A
272 164.56 81.04 Blue B
273 169.15 78.08 Blue B
274 178.99 82.12 Blue B
275 172.16 79.83 Blue B
276 177.58 64.16 Blue A
277 172.11 87.64 Blue A
278 172.05 80.89 Green B
279 158.79 88.85 Grey A
280 164.65 76.36 Grey B
281 158.25 85.47 Blue A
282 161.47 86.85 Grey A
283 168.93 74.24 Blue B
284 173.54 81.79 Grey B
285 168.52 71.50 Grey A
286 175.56 79.94 Blue A
287 171.62 108.83 Blue A
288 181.84 68.46 Brown B
289 158.44 86.19 Blue B
290 176.02 82.23 Green B
291 168.42 84.62 Green B
292 173.19 83.46 Grey B
293 166.54 85.19 Brown B
294 151.38 81.86 Grey A
295 168.90 88.59 Green B
296 172.88 90.38 Blue A
297 163.58 86.98 Green B
298 171.87 72.61 Brown A
299 155.50 86.58 Grey B
300 161.69 77.95 Green A
301 163.56 83.34 Blue A
302 156.77 83.00 Grey A
303 179.06 81.64 Blue B
304 160.63 79.35 Blue A
305 179.69 80.81 Brown B
306 177.41 80.01 Brown B
307 171.50 77.46 Green B
308 165.03 95.09 Grey B
309 165.97 73.05 Blue B
310 174.97 88.43 Brown B
311 166.61 69.08 Green A
312 167.91 87.84 Blue A
313 169.47 56.45 Blue B
314 167.06 72.44 Brown A
315 169.09 85.62 Brown A
316 176.48 84.64 Green B
317 169.26 77.97 Brown A
318 166.44 81.41 Blue B
319 167.66 97.88 Brown B
320 177.46 86.76 Grey A
321 167.35 87.24 Green B
322 172.86 73.35 Grey B
323 177.16 89.08 Grey A
324 165.88 90.44 Green A
325 167.17 85.64 Blue A
326 183.38 55.84 Grey B
327 169.61 84.00 Grey B
328 169.70 85.50 Green A
329 166.65 82.95 Grey B
330 164.89 82.81 Blue B
331 158.82 74.39 Grey B
332 168.01 88.06 Brown A
333 165.09 76.29 Brown B
334 180.56 75.08 Blue B
335 167.27 77.80 Blue A
336 173.88 69.05 Blue B
337 168.97 77.02 Brown A
338 173.34 73.76 Brown B
339 176.46 87.81 Grey A
340 169.78 94.35 Green A
341 169.27 59.98 Grey B
342 173.28 75.23 Green A
343 175.18 97.06 Blue B
344 169.39 73.95 Brown B
345 172.04 70.90 Brown B
346 161.62 96.00 Grey B
347 167.23 89.55 Grey A
348 168.43 76.65 Grey B
349 165.32 81.25 Brown A
350 170.01 70.74 Green A
351 173.34 68.53 Green A
352 176.02 77.40 Blue B
353 180.56 78.09 Blue A
354 170.24 80.80 Blue A
355 158.60 103.87 Green B
356 174.98 78.75 Grey A
357 168.61 72.29 Green B
358 170.10 68.90 Blue A
359 174.01 77.02 Blue A
360 164.99 72.64 Grey B
361 159.98 83.14 Grey B
362 175.54 96.49 Green B
363 179.56 96.62 Grey A
364 165.69 91.31 Blue B
365 173.79 85.11 Green B
366 187.49 100.73 Brown B
367 160.26 76.32 Green A
368 173.90 73.22 Green B
369 172.34 87.56 Brown A
370 167.85 71.15 Brown B
371 164.94 78.22 Blue A
372 168.43 100.49 Green B
373 170.77 61.10 Green A
374 165.16 94.65 Grey B
375 181.06 82.71 Blue B
376 180.98 69.60 Green A
377 165.63 102.78 Brown B
378 173.88 84.07 Blue A
379 161.95 77.01 Green B
380 154.79 90.84 Brown B
381 172.77 86.06 Brown B
382 167.95 80.49 Blue A
383 172.97 101.62 Grey B
384 171.57 87.71 Grey A
385 176.72 75.32 Blue B
386 164.06 87.94 Green A
387 172.79 83.01 Blue B
388 175.86 75.64 Brown B
389 167.42 92.96 Blue B
390 162.53 65.76 Green B
391 168.44 74.42 Green B
392 167.32 84.70 Brown A
393 182.32 69.11 Blue B
394 165.47 77.11 Grey B
395 173.39 78.83 Brown B
396 176.25 63.43 Grey B
397 172.76 78.82 Brown A
398 165.97 87.00 Brown A
399 161.92 72.14 Blue A
400 170.86 74.11 Green A
401 167.52 92.29 Grey A
402 164.94 84.64 Green A
403 168.27 79.70 Blue B
404 171.15 79.21 Grey A
405 175.77 74.46 Blue A
406 168.97 89.02 Brown B
407 158.81 80.27 Blue A
408 174.03 89.98 Brown A
409 169.40 86.23 Grey B
410 165.39 71.14 Grey B
411 169.39 69.60 Blue A
412 169.70 64.77 Grey A
413 169.33 55.84 Green B
414 166.31 66.28 Blue B
415 171.87 82.67 Blue A
416 169.81 85.32 Blue B
417 165.96 98.49 Brown A
418 170.11 82.69 Green A
419 172.79 71.13 Green A
420 151.57 74.58 Green B
421 170.07 77.48 Blue B
422 175.22 86.84 Grey B
423 167.23 83.74 Blue B
424 167.22 71.24 Green B
425 170.32 75.31 Blue B
426 171.78 73.14 Brown B
427 167.27 59.76 Grey A
428 171.14 86.26 Brown A
429 163.64 86.49 Blue A
430 168.21 80.75 Blue A
431 173.15 90.29 Brown B
432 179.22 77.37 Brown A
433 167.71 87.98 Brown A
434 164.39 72.47 Grey B
435 162.67 92.86 Green B
436 167.86 82.60 Brown B
437 175.16 89.60 Blue A
438 171.33 76.94 Grey A
439 170.80 92.12 Blue A
440 153.98 63.60 Blue A
441 176.48 91.12 Brown B
442 165.54 86.03 Grey A
443 170.35 71.17 Grey B
444 164.12 69.42 Green B
445 166.53 92.79 Blue A
446 161.65 80.08 Grey A
447 162.83 71.39 Grey B
448 154.30 73.71 Blue A
449 171.31 96.96 Grey B
450 170.92 92.17 Grey A
451 176.17 80.38 Blue B
452 164.79 85.05 Grey A
453 172.76 89.85 Blue A
454 172.17 90.20 Grey A
455 169.22 80.94 Blue A
456 174.34 89.89 Grey A
457 159.21 85.14 Green A
458 159.25 84.37 Brown B
459 178.79 85.92 Brown B
460 170.75 100.58 Green B
461 174.01 87.50 Green B
462 170.14 60.14 Blue B
463 166.26 92.74 Grey A
464 158.56 86.13 Blue B
465 172.19 66.96 Brown B
466 180.26 58.91 Green A
467 173.94 76.43 Green A
468 174.47 82.83 Brown A
469 174.15 75.78 Green B
470 178.28 77.57 Blue B
471 167.32 76.81 Brown A
472 167.55 74.71 Brown B
473 174.61 80.27 Green B
474 173.82 76.83 Blue A
475 167.19 79.44 Green A
476 177.24 93.01 Blue A
477 176.86 82.12 Green A
478 179.92 65.61 Blue A
479 172.28 93.04 Green A
480 171.46 89.48 Green A
481 172.67 79.50 Green B
482 166.06 77.27 Green B
483 176.50 77.26 Brown B
484 156.14 92.50 Blue A
485 174.33 63.12 Green A
486 165.67 86.60 Brown B
487 182.18 67.37 Green A
488 168.91 86.88 Brown A
489 168.06 81.96 Blue B
490 168.13 89.14 Green A
491 165.28 79.44 Grey B
492 162.20 80.96 Green A
493 168.13 102.88 Grey A
494 167.04 82.09 Brown A
495 171.84 77.24 Grey A
496 184.84 88.92 Green A
497 163.31 75.80 Grey B
498 168.68 62.92 Blue B
499 164.68 87.64 Brown A
500 168.44 80.81 Brown B
501 170.56 79.15 Grey A
502 170.47 80.63 Brown B
503 175.32 78.17 Grey B
504 158.59 74.18 Brown B
505 165.56 80.54 Grey A
506 169.45 94.18 Green A
507 178.75 85.72 Green A
508 162.96 74.55 Grey B
509 178.21 73.44 Blue A
510 174.59 72.40 Blue B
511 165.34 56.60 Blue A
512 163.03 86.26 Brown A
513 169.64 95.38 Grey A
514 164.10 70.94 Blue B
515 176.51 62.65 Green B
516 171.61 78.36 Blue B
517 172.94 84.12 Brown A
518 171.89 87.12 Green B
519 170.93 94.28 Green B
520 177.57 67.06 Green B
521 160.03 78.09 Green B
522 169.60 88.06 Green A
523 173.22 78.78 Grey A
524 170.88 93.96 Blue A
525 176.22 85.53 Grey B
526 161.18 80.51 Brown B
527 177.53 71.20 Green B
528 169.75 59.59 Brown A
529 176.47 72.47 Green A
530 169.93 73.92 Brown B
531 171.35 88.80 Brown B
532 154.61 87.71 Green B
533 169.48 100.93 Blue B
534 159.87 83.71 Brown A
535 181.63 71.47 Blue A
536 172.27 76.68 Green B
537 169.75 91.72 Brown A
538 172.92 84.89 Blue B
539 168.23 96.27 Blue B
540 170.28 99.65 Grey B
541 178.00 93.20 Green B
542 167.68 78.06 Green B
543 178.57 75.86 Grey A
544 161.43 90.47 Blue A
545 168.57 87.13 Green A
546 169.03 78.56 Brown A
547 176.40 69.67 Grey B
548 164.51 73.67 Grey A
549 175.72 98.95 Brown B
550 164.30 86.90 Grey A
551 179.74 75.47 Grey B
552 169.85 89.23 Blue B
553 164.25 87.27 Green A
554 163.10 76.19 Grey B
555 175.64 88.12 Brown B
556 169.75 73.06 Green A
557 163.19 95.33 Brown B
558 163.43 87.91 Grey A
559 170.85 107.88 Brown A
560 175.98 66.96 Grey B
561 174.14 79.59 Grey A
562 164.63 93.77 Brown A
563 171.05 83.14 Grey B
564 175.30 80.91 Blue A
565 171.79 77.92 Green A
566 190.44 81.94 Blue B
567 162.78 81.46 Blue A
568 164.60 77.69 Blue B
569 178.35 67.43 Grey A
570 171.65 78.93 Brown A
571 177.71 89.10 Brown A
572 176.95 78.05 Grey A
573 172.74 70.49 Blue A
574 176.61 77.40 Blue A
575 168.20 77.70 Green B
576 177.16 76.00 Green B
577 163.80 80.86 Blue A
578 175.10 82.01 Grey B
579 163.18 75.15 Blue A
580 163.82 75.95 Blue A
581 177.32 78.83 Grey B
582 174.91 71.80 Grey B
583 166.34 70.16 Green A
584 175.25 65.76 Brown A
585 156.16 86.63 Green B
586 166.14 69.57 Green A
587 161.35 82.06 Blue A
588 164.37 68.86 Green A
589 164.92 76.66 Blue B
590 174.23 82.38 Brown A
591 174.52 70.99 Grey A
592 186.73 77.90 Brown A
593 176.61 66.73 Brown B
594 178.36 79.33 Blue A
595 179.95 88.37 Green A
596 162.99 67.45 Green A
597 161.19 69.84 Blue B
598 166.66 73.27 Blue B
599 166.08 76.23 Grey B
600 162.38 93.61 Green B
601 156.36 93.38 Blue A
602 173.69 82.56 Brown B
603 177.88 71.49 Green A
604 162.75 71.58 Blue B
605 155.25 79.86 Brown B
606 173.30 74.63 Blue B
607 171.15 85.35 Blue A
608 174.29 81.74 Blue B
609 166.11 77.77 Grey B
610 177.69 71.63 Grey A
611 176.83 97.28 Green B
612 173.63 66.37 Grey B
613 168.13 84.93 Green A
614 186.67 89.01 Blue A
615 169.45 91.76 Blue B
616 178.85 64.77 Blue A
617 161.17 68.79 Grey A
618 167.75 63.01 Green B
619 171.41 88.07 Grey B
620 160.24 79.17 Grey A
621 170.00 84.39 Grey B
622 172.43 90.57 Blue A
623 178.24 82.11 Green B
624 174.22 85.25 Brown A
625 180.30 77.02 Green A
626 174.27 89.12 Brown B
627 170.56 82.55 Green B
628 176.39 76.38 Grey B
629 163.32 65.88 Green A
630 170.75 74.43 Grey A
631 160.66 61.51 Blue B
632 172.63 83.80 Brown A
633 166.59 92.43 Blue A
634 169.93 67.27 Green A
635 175.05 77.63 Grey B
636 178.56 60.04 Blue B
637 168.06 66.69 Grey A
638 170.22 73.47 Blue B
639 176.07 75.65 Blue B
640 166.89 70.63 Blue B
641 167.15 62.59 Blue A
642 168.53 79.38 Blue A
643 172.10 74.06 Grey B
644 174.17 63.32 Grey B
645 174.77 87.55 Grey B
646 176.97 80.21 Blue B
647 164.17 79.90 Grey A
648 171.23 71.95 Grey A
649 178.24 71.82 Green A
650 153.72 72.64 Brown B
651 162.70 82.01 Brown B
652 170.51 89.57 Green A
653 163.95 68.58 Brown B
654 162.51 83.46 Grey B
655 164.24 82.45 Brown B
656 167.54 83.40 Brown B
657 180.75 81.15 Blue A
658 169.94 91.08 Brown B
659 174.52 73.70 Brown A
660 163.22 95.60 Brown A
661 175.33 74.50 Green B
662 171.08 62.38 Brown B
663 171.09 77.07 Blue B
664 170.31 66.84 Brown B
665 172.64 95.30 Brown A
666 174.63 76.54 Blue A
667 169.94 84.62 Brown A
668 176.14 63.09 Brown B
669 174.21 66.37 Grey A
670 172.13 84.67 Brown B
671 169.09 84.65 Brown B
672 169.38 74.12 Blue A
673 168.05 82.06 Brown B
674 162.81 88.53 Brown A
675 171.95 88.09 Blue A
676 170.11 73.98 Brown A
677 175.39 91.79 Green A
678 174.19 82.75 Green A
679 167.34 86.30 Brown A
680 168.52 98.53 Blue B
681 176.53 92.44 Brown A
682 166.62 78.45 Blue B
683 161.31 62.22 Grey A
684 166.47 70.96 Blue A
685 180.05 73.98 Blue B
686 168.94 89.70 Green B
687 169.79 80.33 Blue B
688 168.25 74.68 Blue B
689 164.29 82.73 Blue B
690 171.67 91.56 Brown B
691 174.31 77.22 Brown A
692 172.06 71.97 Blue B
693 161.57 72.75 Blue B
694 164.84 76.83 Blue B
695 172.66 67.10 Green B
696 162.87 49.90 Blue B
697 163.19 78.14 Brown A
698 164.02 96.30 Green A
699 183.65 99.65 Brown A
700 175.41 82.76 Brown B
701 174.07 80.72 Blue B
702 174.03 94.90 Brown A
703 167.99 56.45 Brown B
704 173.09 78.02 Green B
705 171.77 99.21 Brown B
706 179.12 73.48 Green B
707 174.09 70.61 Blue A
708 161.14 77.89 Grey A
709 174.88 73.97 Blue A
710 170.58 73.96 Blue B
711 170.48 80.32 Grey B
712 179.76 93.34 Green B
713 170.23 85.36 Blue B
714 168.76 87.17 Blue A
715 172.88 81.29 Green B
716 172.18 89.87 Green B
717 171.80 76.74 Brown B
718 166.94 73.91 Brown B
719 165.70 90.13 Green A
720 171.07 70.05 Blue A
721 164.01 66.34 Blue A
722 168.21 70.46 Brown A
723 171.18 79.93 Brown A
724 164.36 78.43 Brown A
725 166.96 95.54 Blue A
726 163.79 87.12 Blue B
727 165.65 70.37 Brown A
728 175.15 81.44 Grey A
729 174.15 84.45 Brown B
730 180.04 92.50 Green A
731 170.75 92.74 Blue B
732 168.77 88.26 Brown B
733 164.22 71.09 Green B
734 162.97 76.52 Brown A
735 176.71 77.90 Grey A
736 176.80 71.54 Blue B
737 165.90 90.97 Green A
738 172.60 79.67 Blue A
739 167.44 80.15 Grey B
740 165.58 90.47 Blue A
741 173.97 68.93 Green B
742 171.99 75.40 Grey A
743 172.34 78.00 Green A
744 179.89 103.31 Blue B
745 167.02 74.14 Blue A
746 172.16 54.04 Blue B
747 176.38 70.12 Grey A
748 170.93 82.14 Grey B
749 167.08 91.17 Brown B
750 164.93 82.62 Blue A
751 175.88 76.24 Grey B
752 166.28 83.51 Brown B
753 170.95 75.33 Green A
754 179.68 66.80 Green B
755 169.16 93.42 Brown A
756 168.96 90.89 Blue A
757 163.47 93.37 Brown A
758 171.15 71.93 Brown B
759 167.40 75.02 Blue A
760 161.63 102.45 Grey A
761 180.13 77.66 Brown B
762 178.47 80.87 Blue A
763 169.63 75.21 Grey A
764 176.56 86.78 Green A
765 177.74 82.43 Grey B
766 169.19 69.64 Green A
767 164.83 97.09 Brown A
768 163.19 89.89 Blue A
769 165.76 85.69 Blue B
770 173.29 72.52 Green A
771 167.18 77.84 Grey B
772 172.95 78.55 Green B
773 176.74 74.88 Blue A
774 177.22 87.75 Grey B
775 166.53 74.29 Green B
776 160.60 67.70 Green B
777 176.38 88.54 Green A
778 174.40 85.31 Brown A
779 165.25 91.00 Green A
780 177.43 89.33 Blue B
781 167.65 63.56 Green A
782 177.33 94.90 Grey B
783 170.09 86.71 Green A
784 165.35 77.97 Green B
785 170.60 76.48 Grey B
786 162.26 67.41 Green B
787 167.22 84.14 Green B
788 175.02 74.77 Green B
789 168.25 82.26 Brown A
790 179.58 82.23 Brown B
791 166.60 63.60 Grey A
792 183.53 93.09 Green B
793 162.68 87.86 Blue A
794 162.25 78.41 Grey B
795 166.39 86.34 Blue A
796 168.94 76.32 Grey A
797 169.38 66.64 Green A
798 160.81 80.23 Brown A
799 175.86 103.65 Blue A
800 173.55 75.50 Green B
801 175.93 78.76 Brown A
802 174.23 72.99 Green B
803 155.07 78.15 Brown A
804 154.94 91.89 Green A
805 181.97 85.87 Blue B
806 168.37 78.18 Blue B
807 168.38 84.86 Grey B
808 164.10 86.29 Brown B
809 176.51 83.06 Brown B
810 169.17 70.59 Blue A
811 165.30 88.88 Green A
812 152.73 106.71 Grey B
813 162.30 78.38 Grey A
814 169.78 88.09 Green A
815 156.24 69.05 Brown B
816 173.76 84.85 Brown A
817 167.88 68.38 Grey A
818 173.61 80.97 Brown A
819 173.97 65.25 Brown A
820 170.20 72.93 Green A
821 163.11 76.60 Green B
822 168.18 79.78 Green B
823 180.30 74.17 Brown A
824 178.59 108.06 Grey B
825 175.04 93.19 Blue B
826 166.47 83.47 Green B
827 167.79 103.34 Green B
828 168.53 87.19 Green A
829 173.41 85.98 Green A
830 177.26 71.78 Green B
831 165.19 73.09 Grey B
832 160.25 79.25 Brown A
833 166.17 75.82 Blue B
834 165.99 90.73 Brown A
835 174.01 93.04 Grey A
836 170.75 73.70 Green A
837 165.53 76.12 Grey B
838 163.12 79.36 Brown B
839 175.52 104.40 Grey A
840 162.10 82.79 Grey A
841 170.70 81.55 Grey B
842 179.68 80.26 Grey A
843 173.63 74.21 Blue A
844 164.29 95.37 Blue A
845 176.13 65.54 Grey B
846 166.36 95.99 Blue A
847 159.11 95.86 Grey B
848 161.11 82.53 Green A
849 168.29 75.64 Blue B
850 169.12 92.68 Grey A
851 178.47 79.49 Blue A
852 164.98 84.26 Brown B
853 167.15 91.39 Brown A
854 174.75 89.21 Blue A
855 173.06 96.82 Grey A
856 170.89 85.34 Green A
857 176.36 81.04 Green B
858 159.71 89.90 Green B
859 179.42 74.60 Brown A
860 171.31 77.28 Brown A
861 175.87 79.65 Grey B
862 172.01 73.07 Green A
863 172.25 88.08 Green A
864 174.65 103.53 Grey B
865 169.25 87.58 Blue B
866 174.45 76.70 Grey B
867 168.06 73.86 Green A
868 168.20 94.57 Brown B
869 174.37 83.11 Brown B
870 177.28 84.83 Green B
871 161.53 68.31 Blue A
872 176.04 82.64 Blue A
873 168.29 89.21 Brown B
874 171.79 84.39 Grey A
875 161.65 64.42 Grey A
876 167.76 72.40 Blue B
877 165.00 85.91 Blue A
878 169.62 86.85 Green A
879 164.89 86.33 Brown B
880 172.45 92.88 Blue A
881 177.68 82.90 Grey A
882 171.01 73.70 Brown B
883 172.80 70.30 Green A
884 162.82 78.72 Grey A
885 172.07 78.42 Brown B
886 167.53 76.82 Green B
887 166.53 61.72 Brown A
888 175.83 82.41 Brown A
889 175.85 78.54 Blue A
890 172.35 77.06 Green A
891 159.89 72.25 Blue B
892 168.86 74.20 Green A
893 168.82 84.83 Grey B
894 162.43 76.83 Grey A
895 171.67 78.62 Green A
896 170.28 84.15 Grey B
897 164.97 92.02 Grey A
898 173.88 79.34 Grey A
899 169.67 89.66 Blue B
900 161.69 75.16 Blue A
901 172.27 85.13 Brown B
902 169.54 91.62 Green B
903 168.60 77.12 Grey B
904 182.19 95.20 Brown B
905 168.41 96.50 Grey A
906 172.94 88.94 Green A
907 161.49 74.56 Green B
908 173.85 76.79 Green B
909 174.67 68.89 Blue B
910 170.00 79.42 Green B
911 173.66 69.17 Grey A
912 171.71 75.47 Green B
913 176.86 86.89 Brown A
914 177.43 83.44 Grey B
915 176.72 87.39 Grey A
916 163.52 85.04 Green B
917 167.98 64.71 Blue B
918 169.84 68.25 Brown B
919 181.70 86.95 Grey B
920 168.66 87.02 Green A
921 178.01 76.09 Grey B
922 172.97 86.43 Blue A
923 163.88 94.98 Blue A
924 175.91 70.74 Green A
925 175.02 83.33 Grey B
926 166.03 74.03 Grey A
927 168.75 68.48 Grey B
928 169.23 91.66 Grey A
929 180.73 84.52 Blue B
930 171.83 84.99 Brown B
931 175.38 84.91 Brown A
932 174.40 68.84 Grey B
933 169.82 84.77 Grey B
934 167.19 86.10 Brown B
935 179.94 82.12 Blue A
936 164.61 83.94 Brown A
937 165.90 80.76 Green A
938 168.49 62.05 Green A
939 171.94 62.71 Blue A
940 166.10 70.15 Green A
941 179.36 67.38 Grey B
942 170.49 72.80 Green B
943 169.66 72.84 Brown B
944 165.70 67.24 Green B
945 167.07 69.70 Green A
946 167.18 85.68 Green B
947 176.69 71.44 Blue B
948 167.44 82.49 Green B
949 174.51 86.17 Grey A
950 165.77 80.27 Brown B
951 159.22 69.53 Brown A
952 158.99 81.21 Grey A
953 167.96 94.78 Blue B
954 166.47 57.39 Blue A
955 165.49 77.38 Grey B
956 161.26 77.51 Brown A
957 171.96 71.25 Brown B
958 171.74 74.65 Blue B
959 165.00 64.00 Grey A
960 175.32 94.93 Grey A
961 168.47 70.10 Brown A
962 169.96 76.55 Green A
963 159.99 85.83 Brown B
964 182.92 68.42 Blue A
965 166.44 77.82 Grey B
966 168.62 79.84 Grey B
967 172.09 61.65 Blue A
968 175.73 76.45 Brown A
969 168.53 93.80 Blue A
970 156.00 90.44 Grey A
971 166.66 60.89 Brown A
972 161.20 56.18 Green A
973 179.80 77.04 Brown B
974 164.49 82.16 Green A
975 164.97 77.10 Green A
976 166.25 72.15 Blue B
977 165.78 84.93 Blue A
978 159.43 77.98 Green B
979 165.40 108.75 Grey B
980 168.26 83.79 Grey B
981 171.39 91.25 Grey B
982 176.38 70.61 Green A
983 174.40 85.17 Grey A
984 169.76 73.37 Green B
985 158.29 96.39 Grey B
986 177.91 83.13 Grey B
987 167.58 72.57 Green B
988 158.10 67.28 Grey B
989 170.73 95.74 Brown B
990 165.32 89.17 Brown B
991 175.11 72.74 Grey A
992 167.17 88.95 Green B
993 172.26 104.35 Grey A
994 162.35 60.29 Brown A
995 162.48 90.76 Green B
996 174.42 85.16 Blue B
997 169.26 72.03 Brown B
998 178.41 75.57 Grey B
999 167.06 77.55 Blue A
1000 169.07 92.08 Blue B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 170.62 77.78 Brown A
2 174.04 49.24 Brown A
3 171.12 85.96 Grey B
4 166.27 89.28 Grey A
5 169.99 103.33 Brown A
6 165.38 84.37 Brown A
7 171.92 80.29 Green B
8 173.02 97.12 Blue A
9 165.83 91.32 Green A
10 163.81 89.87 Brown A
11 165.78 74.25 Green A
12 175.28 99.72 Grey A
13 171.90 95.85 Blue A
14 171.11 63.92 Brown A
15 167.29 66.29 Grey B
16 167.43 97.85 Blue A
17 166.59 77.91 Grey B
18 169.54 89.53 Grey B
19 162.91 81.23 Brown B
20 156.62 71.98 Grey B
21 168.07 83.66 Brown A
22 167.72 81.11 Blue A
23 173.65 78.10 Green B
24 171.84 74.55 Grey A
25 161.53 70.32 Brown A
26 167.05 90.10 Brown A
27 172.42 88.43 Blue B
28 176.32 63.16 Grey B
29 181.28 87.74 Green B
30 171.20 63.42 Brown A
31 166.78 74.78 Blue B
32 168.40 80.77 Green B
33 167.06 78.07 Grey A
34 162.80 69.65 Blue B
35 154.76 84.17 Brown B
36 163.79 86.04 Brown A
37 158.00 82.08 Green A
38 170.47 68.50 Blue B
39 170.56 77.96 Blue A
40 180.94 94.93 Green A
41 167.84 95.25 Brown A
42 167.48 99.63 Brown A
43 167.45 93.59 Grey A
44 152.83 88.78 Grey B
45 169.91 78.77 Grey A
46 167.39 75.19 Green A
47 163.90 77.07 Grey B
48 171.55 75.64 Green A
49 169.16 90.56 Grey A
50 172.17 72.51 Blue B
51 176.74 81.63 Blue B
52 171.20 76.86 Blue A
53 175.02 97.72 Blue B
54 165.89 87.05 Green A
55 159.78 76.90 Green A
56 169.08 81.10 Brown B
57 172.15 65.48 Brown B
58 165.38 81.77 Green A
59 164.43 81.79 Grey A
60 174.78 74.47 Brown A
61 182.01 74.23 Grey A
62 166.11 79.51 Brown A
63 174.10 90.42 Grey B
64 174.12 82.12 Blue A
65 169.17 91.05 Grey B
66 181.42 77.08 Green A
67 176.10 82.71 Brown A
68 169.15 78.50 Grey A
69 172.27 89.14 Blue A
70 166.27 74.35 Green B
71 168.44 70.31 Green A
72 166.40 95.56 Grey B
73 167.81 72.94 Brown B
74 169.04 86.17 Green B
75 170.34 74.29 Grey B
76 173.59 85.34 Brown A
77 160.20 83.85 Green B
78 163.58 99.63 Blue B
79 170.72 85.68 Grey A
80 165.34 94.12 Brown B
81 177.27 76.52 Green A
82 157.97 69.20 Grey A
83 180.20 93.03 Blue B
84 164.41 80.35 Blue A
85 171.17 87.68 Green A
86 173.12 91.04 Brown B
87 170.82 79.29 Brown A
88 179.01 70.03 Green B
89 173.40 85.50 Grey A
90 153.63 85.02 Blue B
91 157.98 81.01 Grey B
92 177.32 90.66 Grey A
93 169.64 64.72 Green A
94 176.31 79.63 Blue A
95 173.12 87.03 Green A
96 181.55 94.48 Brown B
97 164.51 77.91 Grey B
98 173.67 70.98 Green B
99 185.87 73.14 Blue A
100 175.63 106.73 Green A
101 170.16 63.49 Blue A
102 161.98 92.24 Blue A
103 164.81 64.20 Blue B
104 171.76 91.59 Grey A
105 173.45 79.38 Blue B
106 178.81 85.98 Blue A
107 169.10 92.82 Grey B
108 166.88 91.30 Blue B
109 173.63 78.75 Brown B
110 173.67 54.60 Green B
111 164.05 71.77 Grey B
112 170.56 85.79 Green A
113 161.59 65.32 Green B
114 159.97 79.96 Green B
115 167.57 86.89 Grey B
116 165.20 86.76 Blue A
117 162.48 55.40 Green B
118 179.48 91.55 Blue A
119 167.69 85.30 Blue B
120 164.32 86.76 Blue A
121 176.56 78.42 Green B
122 166.03 68.93 Blue A
123 175.66 91.10 Grey B
124 173.17 95.23 Blue B
125 175.84 100.18 Brown B
126 163.15 75.93 Blue B
127 170.37 86.70 Grey B
128 174.11 85.43 Grey A
129 164.79 85.64 Grey B
130 170.73 76.34 Grey A
131 186.59 70.37 Brown A
132 165.57 75.13 Blue B
133 169.04 67.44 Blue B
134 175.40 101.61 Green A
135 172.84 70.44 Blue B
136 173.65 73.54 Brown B
137 165.04 87.82 Green B
138 178.02 82.15 Brown A
139 170.15 82.39 Grey B
140 167.53 68.22 Green B
141 161.17 86.42 Blue A
142 159.85 76.22 Green B
143 177.30 64.93 Grey A
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448 154.30 73.71 Blue B
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795 166.39 86.34 Blue A
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799 175.86 103.65 Blue A
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816 173.76 84.85 Brown A
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819 173.97 65.25 Brown A
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825 175.04 93.19 Blue B
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832 160.25 79.25 Brown A
833 166.17 75.82 Blue A
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836 170.75 73.70 Green B
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838 163.12 79.36 Brown B
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840 162.10 82.79 Grey B
841 170.70 81.55 Grey A
842 179.68 80.26 Grey A
843 173.63 74.21 Blue B
844 164.29 95.37 Blue A
845 176.13 65.54 Grey B
846 166.36 95.99 Blue B
847 159.11 95.86 Grey B
848 161.11 82.53 Green B
849 168.29 75.64 Blue B
850 169.12 92.68 Grey A
851 178.47 79.49 Blue B
852 164.98 84.26 Brown A
853 167.15 91.39 Brown B
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855 173.06 96.82 Grey B
856 170.89 85.34 Green A
857 176.36 81.04 Green A
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864 174.65 103.53 Grey B
865 169.25 87.58 Blue B
866 174.45 76.70 Grey B
867 168.06 73.86 Green B
868 168.20 94.57 Brown B
869 174.37 83.11 Brown A
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874 171.79 84.39 Grey B
875 161.65 64.42 Grey B
876 167.76 72.40 Blue B
877 165.00 85.91 Blue A
878 169.62 86.85 Green A
879 164.89 86.33 Brown B
880 172.45 92.88 Blue B
881 177.68 82.90 Grey A
882 171.01 73.70 Brown B
883 172.80 70.30 Green A
884 162.82 78.72 Grey A
885 172.07 78.42 Brown B
886 167.53 76.82 Green B
887 166.53 61.72 Brown B
888 175.83 82.41 Brown A
889 175.85 78.54 Blue B
890 172.35 77.06 Green B
891 159.89 72.25 Blue A
892 168.86 74.20 Green A
893 168.82 84.83 Grey A
894 162.43 76.83 Grey A
895 171.67 78.62 Green A
896 170.28 84.15 Grey A
897 164.97 92.02 Grey A
898 173.88 79.34 Grey A
899 169.67 89.66 Blue A
900 161.69 75.16 Blue B
901 172.27 85.13 Brown A
902 169.54 91.62 Green A
903 168.60 77.12 Grey B
904 182.19 95.20 Brown A
905 168.41 96.50 Grey B
906 172.94 88.94 Green B
907 161.49 74.56 Green A
908 173.85 76.79 Green A
909 174.67 68.89 Blue B
910 170.00 79.42 Green B
911 173.66 69.17 Grey B
912 171.71 75.47 Green B
913 176.86 86.89 Brown B
914 177.43 83.44 Grey A
915 176.72 87.39 Grey A
916 163.52 85.04 Green A
917 167.98 64.71 Blue B
918 169.84 68.25 Brown A
919 181.70 86.95 Grey A
920 168.66 87.02 Green A
921 178.01 76.09 Grey B
922 172.97 86.43 Blue A
923 163.88 94.98 Blue B
924 175.91 70.74 Green B
925 175.02 83.33 Grey A
926 166.03 74.03 Grey A
927 168.75 68.48 Grey B
928 169.23 91.66 Grey A
929 180.73 84.52 Blue A
930 171.83 84.99 Brown A
931 175.38 84.91 Brown A
932 174.40 68.84 Grey A
933 169.82 84.77 Grey B
934 167.19 86.10 Brown B
935 179.94 82.12 Blue B
936 164.61 83.94 Brown B
937 165.90 80.76 Green A
938 168.49 62.05 Green B
939 171.94 62.71 Blue B
940 166.10 70.15 Green A
941 179.36 67.38 Grey A
942 170.49 72.80 Green A
943 169.66 72.84 Brown B
944 165.70 67.24 Green A
945 167.07 69.70 Green B
946 167.18 85.68 Green A
947 176.69 71.44 Blue A
948 167.44 82.49 Green B
949 174.51 86.17 Grey A
950 165.77 80.27 Brown A
951 159.22 69.53 Brown B
952 158.99 81.21 Grey A
953 167.96 94.78 Blue A
954 166.47 57.39 Blue B
955 165.49 77.38 Grey B
956 161.26 77.51 Brown B
957 171.96 71.25 Brown B
958 171.74 74.65 Blue A
959 165.00 64.00 Grey A
960 175.32 94.93 Grey A
961 168.47 70.10 Brown A
962 169.96 76.55 Green B
963 159.99 85.83 Brown A
964 182.92 68.42 Blue A
965 166.44 77.82 Grey B
966 168.62 79.84 Grey B
967 172.09 61.65 Blue A
968 175.73 76.45 Brown B
969 168.53 93.80 Blue A
970 156.00 90.44 Grey B
971 166.66 60.89 Brown A
972 161.20 56.18 Green A
973 179.80 77.04 Brown A
974 164.49 82.16 Green B
975 164.97 77.10 Green A
976 166.25 72.15 Blue B
977 165.78 84.93 Blue A
978 159.43 77.98 Green B
979 165.40 108.75 Grey B
980 168.26 83.79 Grey A
981 171.39 91.25 Grey A
982 176.38 70.61 Green B
983 174.40 85.17 Grey B
984 169.76 73.37 Green A
985 158.29 96.39 Grey A
986 177.91 83.13 Grey B
987 167.58 72.57 Green A
988 158.10 67.28 Grey B
989 170.73 95.74 Brown B
990 165.32 89.17 Brown B
991 175.11 72.74 Grey B
992 167.17 88.95 Green B
993 172.26 104.35 Grey A
994 162.35 60.29 Brown A
995 162.48 90.76 Green A
996 174.42 85.16 Blue A
997 169.26 72.03 Brown A
998 178.41 75.57 Grey B
999 167.06 77.55 Blue B
1000 169.07 92.08 Blue A

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.